Background: Neutron-rich nuclei with mass number between 100 and 110 attract much attention, since several kinds of shapes, such as spherical, prolate, oblate, and triaxial shapes, are predicted. In particular, for neutron-rich Mo isotopes, different models predict different magnitudes and rigidity of triaxial deformation. Previous interpretations of experimental results based solely on low-lying 2⁺₂ states are insufficient to distinguish between the rigid triaxial shape, γ vibration, or γ -soft rotor.

Purpose: The shape evolution of ¹⁰⁶Mo, ¹⁰⁸Mo, and ¹¹⁰Mo is investigated through their 2⁺₁-state lifetimes, decay-branching ratios of the 2⁺₂ state, and energies of the low-lying collective excited states with K^π = 0⁺, 2⁺, and 4⁺.

Method: β -delayed γ -ray spectroscopy was employed for neutron-rich Nb and Zr isotopes produced at the RIKEN RI Beam Factory to populate excited states in ¹⁰⁶Mo , ¹⁰⁸Mo , and ¹¹⁰Mo . The EUroball-RIKEN Cluster Array was used for high-resolution γ -ray detection and lifetimes of the 2⁺₁ states were determined using the UK fast-timing array of LaBr₃(Ce) detectors.

Results: New γ -ray transitions and levels are reported, including newly assigned 0⁺₂ states in ^108,110Mo . Quadrupole deformations were obtained for ^106,108,110Mo from their 2⁺₁ energies and lifetimes. The β -delayed neutron-emission probabilities of 108 Nb and 110 Nb were determined by examining the γ rays of their respective daughter decays.

Conclusions: The even-odd energy staggering in the 2⁺₂ band was compared with typical patterns of the γ -vibrational band, rigid triaxial rotor, and γ -soft rotor. The very small even-odd staggering of ¹⁰⁶ Mo, ¹⁰⁸Mo, and ¹¹⁰Mo favors a γ -vibrational band assignment. The kinematic moment of inertia for the 2⁺₂ band showed a trend similar to the ground-state band, which is as expected for the γ -vibrational band. Beyond-mean-field calculations employing the constrained Hartree-Fock-Bogoliubov and local quasiparticle-random-phase approximation method using the SLy 5 + T interaction reproduced the ground and 2⁺₂ bands in ¹⁰⁶Mo and ¹⁰⁸Mo . The collective wave functions are consistent with the interpretation of the 2⁺₂ band as the γ -vibrational band of the prolate shape. However, the staggering pattern observed in ¹¹⁰Mo differs from the one suggested in the calculations which predict a γ -soft rotor. There was no experimental indication of the oblate shape or the γ -soft rotor predicted in these Mo isotopes.